Blowup phenomenon for the initial-boundary value problem of the non-isentropic compressible Euler equations

2018 ◽  
Vol 59 (4) ◽  
pp. 041502 ◽  
Author(s):  
Ka Luen Cheung ◽  
Sen Wong ◽  
Manwai Yuen
Keyword(s):  
Boundary Value Problem ◽  
Euler Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Initial Boundary Value

scholarly journals Blowup Phenomenon of Solutions for the IBVP of the Compressible Euler Equations in Spherical Symmetry

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Ka Luen Cheung ◽  
Sen Wong
Keyword(s):  
Positive Integer ◽  
Boundary Value Problem ◽  
Euler Equations ◽  
Spherical Symmetry ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressible Euler Equations ◽  
Compressible Euler ◽  
Isothermal Case ◽  
Initial Boundary Value

The blowup phenomenon of solutions is investigated for the initial-boundary value problem (IBVP) of theN-dimensional Euler equations with spherical symmetry. We first show that there are only trivial solutions when the velocity is of the formc(t)xα-1x+b(t)(x/x)for any value ofα≠1or any positive integerN≠1. Then, we show that blowup phenomenon occurs whenα=N=1andc2(0)+c˙(0)<0. As a corollary, the blowup properties of solutions with velocity of the form(a˙t/at)x+b(t)(x/x)are obtained. Our analysis includes both the isentropic case(γ>1)and the isothermal case(γ=1).

On the initial-boundary value problem for the Euler equations in presence of a rarefaction wave

2019 ◽  
Vol 16 (02) ◽  
pp. 271-292
Author(s):  
Dening Li
Keyword(s):  
Boundary Value Problem ◽  
Rarefaction Wave ◽  
Euler Equations ◽  
Smooth Solution ◽  
Infinite Order ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Classical Sense ◽  
Initial Boundary Value

We study the initial-boundary value problem for the general non-isentropic 3D Euler equations with data which are incompatible in the classical sense, but are “rarefaction-compatible”. We show that such data are also rarefaction-compatible of infinite order and the initial-boundary value problem has a piece-wise smooth solution containing a rarefaction wave.

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